arXiv subjects

Nicholas Loutrel

Publications and source records attributed to Nicholas Loutrel.

At least 19 recordsLinked to original sources

arXiv2025

Probing modified gravitational-wave dispersion with bursts from eccentric black-hole binaries

Gravitational waves in general relativity are non-dispersive, yet a host of modified theories predict dispersion effects during propagation. In this work, we consider the impact of dispersion effects on gravitational-wave bursts from highly eccentric binary black holes. We consider the dispersion effects within the low-energy, effective field theory limit, and model the dispersion relation via standard parameterized deformations. Such modified dispersion relations produce two modifications to the burst waveform: a modification to the time of arrival of the bursts in the detector, which appears as a 2.5PN correction to the difference in burst arrival times, and a modification to the arrival time of individual orbital harmonics within the bursts themselves, resulting in a Bessel-type amplitude modulation of the waveform. Using the Fisher information matrix, we study projected constraints one might obtain with future observations of repeating burst signals with LIGO. We find that the projected constraints vary significantly depending on the theoretical mechanism producing the modified dispersion. For massive gravitons and multifractional spacetimes that break Lorentz invariance, bounds on the coupling parameters are generally weaker than current bounds. For other Lorentz invariance breaking models such as Ho\v{r}ava-Lifschitz gravity, as well as scenarios with extra dimensions, the bounds in optimal cases can be 1-3 orders of magnitude stronger than current bounds.

gr-qc↗

arXiv2025

PRECESSION 2.1: black-hole binary spin precession on eccentric orbits

We present version 2.1 of the public code {\sc precession}, a Python module for studying the post-Newtonian dynamics of precessing black hole binaries. In this release, we extend the code to handle eccentric orbits. This extension leverages the existing numerical infrastructure wherever possible, introducing a semi-automatic method to adapt circular-orbit functions to the eccentric case via a Python decorator. Additional new features include orbit- and precession-averaged evolutionary equations for the eccentricity, as well as revised expressions to convert between post-Newtonian separation and gravitational-wave emission frequency.

gr-qc↗

arXiv2025

Non-adiabatic dynamics of eccentric black-hole binaries in post-Newtonian theory

Eccentric black-hole binaries are among the most awaited sources of gravitational waves, yet their dynamics lack a consistent framework that provides a detailed and physically robust evolutionary description due to gauge issues. We present a new set of non-orbit-averaged equations, free from radiation-reaction gauge ambiguities, that accurately describe the evolution of orbital elements for eccentric, non-spinning black-hole binaries. We derive these equations by mapping the Keplerian orbital elements to a new set of characteristic parameters using energy and angular momentum definitions combined with near-identity transformations. The resulting framework is valid for arbitrary eccentricities, including parabolic and hyperbolic limits. Using this framework, we demonstrate the strictly observable effects of the non-adiabatic emission of gravitational waves -- characteristic of eccentric binaries -- on the orbital parameters. Furthermore, we assess the regime of validity of the widely used orbit-averaged equations first derived by Peters in 1964. Importantly, their breakdown becomes evident at the first pericenter passage, implying that the validity of the orbit-averaged approximation cannot be inferred solely from binary initial conditions. The formalism we introduce, accurate up to 2.5 post-Newtonian order, aims to provide a robust tool for making reliable astrophysical predictions and accurately interpreting current and future gravitational wave data, paving the way for deeper insights into the dynamics of eccentric black hole binaries.

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arXiv2024

Orbital eccentricity in general relativity from catastrophe theory

While the orbital eccentricity is a key feature of the gravitational two-body problem, providing an unambiguous definition in general relativity poses significant challenges. Despite such foundational issue, the eccentricity of binary black holes has important implications in gravitational-wave astronomy. We present a novel approach to consistently define the orbital eccentricity in general relativity, grounded in the mathematical field of catastrophe theory. Specifically, we identify the presence of catastrophes, i.e., breakdowns of the stationary-phase approximation, in numerical relativity waveforms and exploit them to develop a robust and fully gauge-invariant estimator of the eccentricity. Our procedure does not require orbital fitting and naturally satisfies the Newtonian limit. The proposed eccentricity estimator agrees with and generalizes a previous proposal, though with a fully independent derivation. We extract gauge-free eccentricity estimates from about 100 numerical relativity simulations and find that the resulting values are systematically lower compared to those reported alongside the simulations themselves.

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arXiv2024

Analytical model of precessing binaries using post-Newtonian theory in the extreme mass-ratio limit I: General Formalism

We develop a fully analytical waveform model for precessing binaries with arbitrary spin vectors using post-Newtonian~(PN) theory in the extreme mass-ratio limit and a hierarchical multi-scale analysis. The analytical model incorporates leading PN order spin precession dynamics from spin-orbit, spin-spin, and quadrupole-monopole couplings, and 2PN order dissipative dynamics truncated to first order in the mass ratio $q \ll 1$. Due to the pure analytic nature of the model, the framework developed herein can readily be extended to both higher PN and higher-$q$ order. Although the PN series is asymptotic to this limit, our results can be used to estimate how precession affects the measurability of certain binary parameters, and to inform and compare with other waveform approximants, such as effective-one-body models, hybrid waveforms, and self-force calculations.

gr-qc↗

arXiv2023

Relevance of Precession for Tests of the Black Hole No Hair Theorems

The multipole moments of black holes in general relativity obey certain consistency relations known as the no-hair theorems. The details of this multipolar structure are imprinted into the gravitational waves emitted by binary black holes, particularly if the binary is precessing. If black holes do not obey the vacuum field equations of general relativity, then the no-hair theorems may be broken, and the observed gravitational waves will be modified, thus providing an important test of the no-hair theorems. Recently, analytic solutions to the precession dynamics and inspiral waveforms were computed within the context of binaries possessing non-axisymmetric mass quadrupole moments, which are parametrized by a modulus $q_{m}$ and phase $a_{m}$ with $m = 1,2$ the azimuthal spherical harmonic number. Here, we use a Fisher analysis to study plausible constraints one may obtain on generic, non-axisymmetry quadrupole configurations using current and future ground-based detectors. For non-precessing binaries, we generically find that no meaningful constraints can be placed with current detectors on the non-axisymmetry parameters $(q_{m}, a_{m})$ due to the presence of strong degeneracies with other waveform parameters, while with next generation detectors, only weak constraints are possible. For precessing configurations, the exact value of the uncertainty is strongly dependent on the sky location, system orientation relative to the line of sight, and initial inclination angle of the orbital angular momentum. After averaging over these parameters, we find that with GWTC-3-like events, one should be able to plausibly constraint non-axisymmetric mass quadrupole deviations to $\Delta q_{m} \sim 10^{-2}$ for LIGO at design sensitivity, and $\Delta q_{m} \sim 10^{-4}$ for the same sources with Einstein Telescope and Cosmic Explorer.

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arXiv2023

Eccentric Catastrophes & What To Do With Them

Analytic modeling of gravitational waves from inspiraling eccentric binaries poses an interesting mathematical challenge. When constructing analytic waveforms in the frequency domain, one has to contend with the fact that the phase of the Fourier integral in non-monotonic, resulting in a breakdown of the standard stationary phase approximation. In this work, we study this breakdown within the context of catastrophe theory. We find that the stationary phase approximation holds in the context of eccentric Keplerian orbits when the Fourier frequency satisfies $f_{\rm min} < f < f_{\rm max}$, where $f_{\rm min/max}$ are integer multiples of the apocenter/pericenter frequencies, respectively. For values outside of this interval, the phase undergoes a fold catastrophe, giving rise to an Airy function approximation of the Fourier integral. Using these two different approximations, we generate a matched asymptotic expansion that approximates generic Fourier integrals of Keplerian motion for bound orbits across all frequency values. This asymptotic expansion is purely analytic and closed-form. We discuss several applications of this investigation and the resulting approximation, specifically: 1) the development and improvement of effective fly-by waveforms for binary black holes, 2) the transition from burst emission in the high eccentricity limit to wave-like emission in the quasi-circular limit, which results in an analogy between eccentric gravitational wave bursts and Bose-Einstein condensates, and 3) the calculation of f-mode amplitudes in eccentric binary neutron stars and black hole-neutron star binaries in terms of complex Hansen coefficients. The techniques and approximations developed herein are generic, and will be useful for future studies of gravitational waves from eccentric binaries within the context of post-Newtonian theory.

gr-qc↗

arXiv2022

Eccentricity or spin precession? Distinguishing subdominant effects in gravitational-wave data

Eccentricity and spin precession are key observables in gravitational-wave astronomy, encoding precious information about the astrophysical formation of compact binaries together with fine details of the relativistic two-body problem. However, the two effects can mimic each other in the emitted signals, raising issues around their distinguishability. Since inferring the existence of both eccentricity and spin precession simultaneously is -- at present -- not possible, current state-of-the-art analyses assume that either one of the effects may be present in the data. In such a setup, what are the conditions required for a confident identification of either effect? We present simulated parameter inference studies in realistic LIGO/Virgo noise, studying events consistent with either spin precessing or eccentric binary black hole coalescences and recovering under the assumption that either of the two effects may be at play. We quantify how the distinguishability of eccentricity and spin precession increases with the number of visible orbital cycles, confirming that the signal must be sufficiently long for the two effects to be separable. The threshold depends on the injected source, with inclination, eccentricity, and effective spin playing crucial roles. In particular, for injections similar to GW190521, we find that it is impossible to confidently distinguish eccentricity from spin precession.

astro-ph.HE↗

arXiv2022

Inferring Interference: Identifying a Perturbing Tertiary with Eccentric Gravitational Wave Burst Timing

[Abridged] Binary black holes may form and merge dynamically. These binaries are likely to become bound with high eccentricities, resulting in a burst of gravitational radiation at their point of closest approach. When such a binary is perturbed by a third body, the evolution of the orbit is affected, and gravitational-wave burst times are altered. The bursts times therefore encode information about the tertiary. In order to extract this information, we require a prescription for the relationship between the tertiary properties and the gravitational-wave burst times. In this paper, we demonstrate a toy model for the burst times of a secular three-body system. We show how Bayesian inference can be employed to deduce the tertiary properties when the bursts are detected by next-generation ground-based gravitational-wave detectors. We study the bursts from an eccentric binary with a total mass of $60$~M$_\odot$ orbiting an $6 \times 10^{8}$~M$_\odot$ supermassive black hole. When we assume no knowledge of the eccentric binary, we are unable to tightly constrain the existence or properties of the tertiary, and we recover biased posterior probability distributions for the parameters of the eccentric binary. However, when the properties of the binary are already well-known -- as is likely if the late inspiral and merger are also detected -- we are able to more accurately infer the mass of the perturber, $m_3$, and its distance from the binary, $R$. When we assume measurement precision on the binary parameters consistent with expectations for next-generation gravitational-wave detectors, we can be greater than $90\%$ confident that the binary is perturbed. [...]

gr-qc↗

arXiv2022

Parameterized Post-Einsteinian Framework for Precessing Binaries

In general relativity, isolated black holes obey the no hair theorems, which fix the multipolar structure of their exterior spacetime. However, in modified gravity, or when the compact objects are not black holes, the exterior spacetime may have a different multipolar structure. When two black holes are in a binary, this multipolar structure determines the morphology of the dynamics of orbital and spin precession. In turn, the precession dynamics imprint onto the gravitational waves emitted by an inspiraling compact binary through specific amplitude and phase modulations. The detection and characterization of these amplitude and phase modulations can therefore lead to improved constraints on fundamental physics with gravitational waves. Recently, analytic precessing waveforms were calculated in two scenarios: (i) dynamical Chern-Simons gravity, where the no-hair theorems are violated, and (ii) deformed compact objects with generic mass quadrupole moments. In this work, we use these two examples to propose an extension of the parameterized post-Einsteinian~(ppE) framework to include precession effects. The new framework contains $2n$ ppE parameters $(\mathscr{b}^{\rm ppE}_{(m',n)}, b^{\rm ppE}_{(m',n)})$ for the waveform phase, and $2n$ ppE parameters $(\mathscr{a}^{\rm ppE}_{(m',n)}, a^{\rm ppE}_{(m',n)})$ for the waveform amplitudes. The number of ppE corrections $n$ corresponds to the minimum number of harmonics necessary to achieve a given likelihood threshold when comparing the truncated ppE waveform with the exact one, and $(m',n)$ corresponds to the harmonic numbers of the harmonics containing ppE parameters. We show explicitly how these ppE parameters map to the specific example waveforms discussed above. The proposed ppE framework can serve as a basis for future tests of general relativity with gravitational waves from precessing binaries.

gr-qc↗

arXiv2022

Parity Violation in Spin-Precessing Binaries: Gravitational Waves from the Inspiral of Black Holes in Dynamical Chern-Simons Gravity

Spin precession in compact binaries is intricately tuned to the multipole structure of the underlying bodies. For black holes, violations of the no-hair theorems induced by modifications to general relativity correct the precession dynamics, which in turn imprints onto the amplitude and phase modulations of the gravitational waves emitted by the binary. Recently, the spin precession equations were derived up to second order in spin for dynamical Chern-Simons gravity, a parity violating modified theory of gravity. We here solve these equations and construct, for the first time, analytic expressions for the time- and frequency-domain gravitational waves emitted in the quasi-circular inspiral of spin-precessing black hole binaries in a modified theory of gravity using the post-Newtonian approximation. Working within the small coupling approximation and using multiple scale analysis, we show that the corrections to the nutation phase enter at relative 1PN order, and the corrections to the precession angle and Thomas phase enter at relative 0PN order. Making use of the stationary phase approximation and shifted uniform asymptotics, we find that the Fourier phase of the waveform is characterized by three modifications, two due to the back-reaction of the precession dynamics onto the spin-orbit and spin-spin couplings that enter at 1.5PN and 2PN orders, and a 2PN modification due to the emission of dipole radiation. We also find that back-reaction of the precession dynamics forces the dCS corrections to the Fourier amplitude to enter at 0PN order, as opposed to 2PN order, as expected for spin-aligned binaries. Our work lays the first foundational stones to build an inspiral-merger-ringdown phenomenological model for spin-precessing binaries in a modified theory of gravity.

gr-qc↗

arXiv2022

Inspiralling compact objects with generic deformations

Self-gravitating bodies can have an arbitrarily complex shape, which implies a much richer multipolar structure than that of a black hole in General Relativity. With this motivation, we study the corrections to the dynamics of a binary system due to generic, nonaxisymmetric mass quadrupole moments to leading post-Newtonian (PN) order. Utilizing the method of osculating orbits and a multiple scale analysis, we find analytic solutions to the precession and orbital dynamics of a (generically eccentric) binary in terms of the dimensionless modulus parameters $\epsilon_{m}$, corresponding to axial $m=1$ and polar $m=2$ corrections from oblateness/prolateness. The solutions to the precession dynamics are exact for $0 \le \epsilon_{2} < 1$, and perturbative in $\epsilon_{1} \ll 1$. We further compute the leading order corrections to the gravitational wave amplitude and phase for a quasi-circular binary due to mass quadrupole effects. Making use of the stationary phase approximation and shifted uniform asymptotics (SUA), the corrections to the phase enter at relative 2PN order, while the amplitude modulations enter at -0.5PN order with a SUA amplitude correction at 3.25PN order, relative 2PN order to the leading order SUA correction. By investigating the dephasing due to generic quadrupole moments, we find that a phase difference $\gtrsim 0.1$~radians is achievable for $\epsilon_{m} \gtrsim 10^{-3}$, which suggests that constraints with current and future ground-based gravitational wave detectors are possible. Our results can be implemented in parameter estimation studies to constrain generic multipolar deformations of the Kerr geometry and of neutron stars.

gr-qc↗

arXiv2021

How to assess the primordial origin of single gravitational-wave events with mass, spin, eccentricity, and deformability measurements

A population of primordial black holes formed in the early Universe could contribute to at least a fraction of the black-hole merger events detectable by current and future gravitational-wave interferometers. With the ever-increasing number of detections, an important open problem is how to discriminate whether a given event is of primordial or astrophysical origin. We systematically present a comprehensive and interconnected list of discriminators that would allow us to rule out, or potentially claim, the primordial origin of a binary by measuring different parameters, including redshift, masses, spins, eccentricity, and tidal deformability. We estimate how accurately future detectors (such as the Einstein Telescope and LISA) could measure these quantities, and we quantify the constraining power of each discriminator for current interferometers. We apply this strategy to the GWTC-3 catalog of compact binary mergers. We show that current measurement uncertainties do not allow us to draw solid conclusions on the primordial origin of individual events, but this may become possible with next-generation ground-based detectors.

astro-ph.CO↗

arXiv2021

Neutron Stars in the Effective Fly-By Framework: $f$-Mode Re-summation

Eccentric compact binaries pose not only a challenge for gravitational wave detectors, but also provide a probe into the nuclear equation of state if one of the objects is a neutron star. At the short pericenter passage, tidal interactions excite f-modes on the star, which in turn emit their own gravitational waves. We derive an analytic waveform for these stellar oscillations within the effective fly-by framework, modeling the emission to leading post-Newtonian order. At this order, the f-mode response can be written in a Fourier decomposition in terms of orbital harmonics, with the amplitudes of each harmonic depending on Hansen coefficients. Re-summing the harmonics of the f-mode results in a simple decaying harmonic oscillator, with the amplitude now determined by a Hansen coefficient of complex harmonic number. We compute the match between the re-summed f-mode and numerical integrations of the tidal response, and find ${\cal{M}} > 0.98$ for systems with high orbital eccentricity $(e > 0.8)$ and low semi-latus rectum $(p < 15M)$ for three equations of state. We further compare our model to modes generated from subsequent pericenter passages under the effect of radiation reaction, and develop an accurate model to time pericenter passages. We show how the timing model can be used to specify initial conditions to accurately track the f-mode excitation across multiple pericenter passages.

gr-qc↗

arXiv2020

Deep Learning with Quantized Neural Networks for Gravitational Wave Forecasting of Eccentric Compact Binary Coalescence

We present the first application of deep learning forecasting for binary neutron stars, neutron star - black hole systems, and binary black hole mergers that span an eccentricity range e <= 0.9. We train neural networks that describe these astrophysical populations, and then test their performance by injecting simulated eccentric signals in advanced LIGO noise available at the \texttt{Gravitational Wave Open Science Center} to: 1) quantify how fast neural networks identify these signals before the binary components merge; 2) quantify how accurately neural networks estimate the time to merger once gravitational waves are identified; and 3) estimate the time-dependent sky localization of these events from early detection to merger. Our findings show that deep learning can identify eccentric signals from a few seconds (for binary black holes) up to tens of seconds (for binary neutron stars) prior to merger. A quantized version of our neural networks achieves 4x reduction in model size, and up to 2.5x inference speed up. These novel algorithms may be used to facilitate time-sensitive multi-messenger astrophysics observations of compact binaries in dense stellar environments.

gr-qc↗

arXiv2020

Numerical computation of second order vacuum perturbations of Kerr black holes

Motivated by the desire to understand the leading order nonlinear gravitational wave interactions around arbitrarily rapidly rotating Kerr black holes, we describe a numerical code designed to compute second order vacuum perturbations on such spacetimes. A general discussion of the formalism we use is presented in (arXiv:2008.11770); here we show how we numerically implement that formalism with a particular choice of coordinates and tetrad conditions, and give example results for black holes with dimensionless spin parameters $a=0.7$ and $a=0.998$. We first solve the Teukolsky equation for the linearly perturbed Weyl scalar $\Psi_4^{(1)}$, followed by direct reconstruction of the spacetime metric from $\Psi_4^{(1)}$, and then solve for the dynamics of the second order perturbed Weyl scalar $\Psi_4^{(2)}$. This code is a first step toward a more general purpose second order code, and we outline how our basic approach could be further developed to address current questions of interest, including extending the analysis of ringdown in black hole mergers to before the linear regime, exploring gravitational wave "turbulence" around near-extremal Kerr black holes, and studying the physics of extreme mass ratio inspiral.

gr-qc↗

arXiv2020

Repeated Bursts: Gravitational Waves from Highly Eccentric Binaries

Compact object binaries formed from dynamics interactions will generically have non-zero orbital eccentricity. The gravitational waves from such binaries can change drastically depending on how large the eccentricity is, ranging from emitted in small a subset of orbital harmonics at low eccentricities, to being concentrated into intense bursts of radiation from each pericenter passage at large eccentricities. Gravitational waves from such highly eccentric binaries present themselves an intriguing systems for probing fundamental physics, but also present interesting challenges in terms of detection. The presence of orbital eccentricity in the gravitational wave signature gives an unequivocal method of determining the origin of the binary, while the highly dynamical nature of pericenter passage often enhances the physics associated with matter and gravity. The generation of faithful models of the repeated burst signals has proven challenging, and often sub-optimal detection strategies like power stacking are considered for detection. This chapter reviews our current understanding of eccentric binaries, the leading efforts to model their gravitational wave emission, and the physics that can be probed with these detections.

gr-qc↗

arXiv2020

Second Order Perturbations of Kerr Black Holes: Reconstruction of the Metric

Motivated by gravitational wave observations of binary black hole mergers, we present a procedure to compute the leading order nonlinear gravitational wave interactions around a Kerr black hole. We describe the formalism used to derive the equations for second order perturbations. We develop a procedure that allows us to reconstruct the first order metric perturbation solely from knowledge of the solution to the first order Teukolsky equation, without the need of Hertz potentials. Finally, we illustrate this metric reconstruction procedure in the asymptotic limit for the first order quasi-normal modes of Kerr. In a companion paper, we present a numerical implementation of these ideas.

gr-qc↗